A209401 Number of noncommutative rings with n elements.

0, 0, 0, 2, 0, 0, 0, 18, 2, 0, 0, 4, 0, 0, 0, 228, 0, 4, 0, 4, 0, 0, 0, 36, 2, 0, 23, 4, 0, 0, 0

Offset

1,4

Comments

a(n)=0 if and only if n is squarefree.

Links

Table of n, a(n) for n=1..31.

Gregory Dresden, Rings of Size Four, demonstrating that a(4)=2.

Formula

a(n) = A027623(n) - A037289(n).

Example

For n=8, there are 52 rings of order 8, 18 of which are noncommutative, so a(8)=18.

Crossrefs

Cf. A027623, A037289, A037291.

Sequence in context: A283950 A342376 A277443 * A029696 A118887 A372353

Adjacent sequences: A209398 A209399 A209400 * A209402 A209403 A209404

Keyword

nonn,nice,hard,more

Author

Ben Branman, Mar 26 2012

Status

approved